Problem: Simplify the following expression: $p = \dfrac{-8k^2 + 16k + 280}{k + 5} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-8$ , so we can rewrite the expression: $ p =\dfrac{-8(k^2 - 2k - 35)}{k + 5} $ Then we factor the remaining polynomial: $k^2 {-2}k {-35} $ ${5} {-7} = {-2}$ ${5} \times {-7} = {-35}$ $ (k + {5}) (k {-7}) $ This gives us a factored expression: $\dfrac{-8(k + {5}) (k {-7})}{k + 5}$ We can divide the numerator and denominator by $(k - 5)$ on condition that $k \neq -5$ Therefore $p = -8(k - 7); k \neq -5$